Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. The Howard methods also assume that the species composition of the harvests are equal to the species composition of released fish, which may not be true and is evident in the logbook data. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases. Key advantages of the Bayesian approach are highlighted in table 1.

Example Table
Issue Howard Bayes
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds that when not met, values are borrowed from nearby areas Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is no uncertainty generated from uncertainty in the assmptions made such as species composition of the releases or when borrowing values from one area to another. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.
Time series 1999 - present 1977 - present

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was explored that loosened the assumption that logbook releases were a census. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Priors.

Priors range from uninformative to very informative or fixed. These will be covered once a satisfactorilly convergerd model is achieved.

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behavior and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 8.**- DSR rockfish (including yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (including yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 10.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 10.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 12.**- Residuals from logbook harvests

Figure 12.- Residuals from logbook harvests


SWHS residuals

**Figure 13.**- Residuals from SWHS harvests.

Figure 13.- Residuals from SWHS harvests.



**Figure 14.**- Residual of SWHS releases

Figure 14.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 15.**- Mean percent of harvest by charter anglers.

Figure 15.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 16.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 18.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 18.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 19.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 19.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 20.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 20.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 23.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 23.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 24.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 24.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 25.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 25.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 26.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 26.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 27.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 27.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 28.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 28.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 30.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 30.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 31.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 31.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_pH 1 2.342741
beta3_pH 1 1.959736
beta1_pH 2 1.924829
tau_beta0_pH 1 1.406081
beta2_pH 4 1.310453
beta2_pelagic 2 1.292912
parameter n badRhat_avg
beta0_pelagic 2 1.274682
beta1_pelagic 3 1.270413
beta2_yellow 2 1.220139
beta1_yellow 1 1.178766
tau_beta0_pelagic 1 1.129067
Table 2. Summary of unconverged parameters by area
afognak CI CSEO PWSI PWSO SOKO2SAP WKMA
beta0_pelagic 0 0 0 1 1 0 0
beta0_pH 0 1 0 0 0 0 0
beta1_pelagic 0 0 1 1 1 0 0
beta1_pH 0 1 0 0 1 0 0
beta1_yellow 1 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 1 0 0
beta2_pH 0 1 0 1 1 0 1
beta2_yellow 0 0 0 0 1 1 0
beta3_pH 0 1 0 0 0 0 0
tau_beta0_pelagic 0 1 0 0 0 0 0
tau_beta0_pH 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.127 0.074 -0.263 -0.130 0.026
mu_bc_H[2] -0.096 0.044 -0.173 -0.100 0.000
mu_bc_H[3] -0.434 0.071 -0.573 -0.437 -0.288
mu_bc_H[4] -0.982 0.190 -1.371 -0.980 -0.610
mu_bc_H[5] 0.928 0.936 -0.157 0.745 3.327
mu_bc_H[6] -2.173 0.330 -2.822 -2.181 -1.481
mu_bc_H[7] -0.453 0.110 -0.675 -0.449 -0.247
mu_bc_H[8] 0.245 0.361 -0.370 0.208 1.015
mu_bc_H[9] -0.297 0.135 -0.562 -0.300 -0.030
mu_bc_H[10] -0.106 0.070 -0.237 -0.109 0.037
mu_bc_H[11] -0.122 0.038 -0.197 -0.122 -0.048
mu_bc_H[12] -0.253 0.107 -0.480 -0.251 -0.052
mu_bc_H[13] -0.134 0.078 -0.290 -0.134 0.018
mu_bc_H[14] -0.299 0.096 -0.503 -0.300 -0.119
mu_bc_H[15] -0.344 0.051 -0.442 -0.344 -0.241
mu_bc_H[16] -0.254 0.367 -0.906 -0.283 0.566
mu_bc_R[1] 1.346 0.146 1.060 1.343 1.640
mu_bc_R[2] 1.451 0.091 1.275 1.450 1.630
mu_bc_R[3] 1.392 0.142 1.113 1.393 1.662
mu_bc_R[4] 0.899 0.204 0.479 0.906 1.272
mu_bc_R[5] 1.140 0.483 0.145 1.147 2.072
mu_bc_R[6] -1.596 0.421 -2.427 -1.601 -0.778
mu_bc_R[7] 0.264 0.177 -0.087 0.263 0.610
mu_bc_R[8] 0.554 0.200 0.144 0.561 0.917
mu_bc_R[9] 0.328 0.206 -0.123 0.339 0.688
mu_bc_R[10] 1.296 0.137 1.020 1.297 1.556
mu_bc_R[11] 1.039 0.098 0.842 1.040 1.233
mu_bc_R[12] 0.828 0.209 0.394 0.833 1.235
mu_bc_R[13] 1.025 0.105 0.820 1.026 1.231
mu_bc_R[14] 0.900 0.141 0.617 0.902 1.169
mu_bc_R[15] 0.783 0.111 0.569 0.782 1.005
mu_bc_R[16] 1.094 0.128 0.833 1.094 1.347
tau_pH[1] 5.236 0.457 4.372 5.217 6.167
tau_pH[2] 2.054 0.218 1.645 2.047 2.503
tau_pH[3] 2.156 0.257 1.675 2.146 2.665
beta0_pH[1,1] 0.526 0.173 0.177 0.528 0.860
beta0_pH[2,1] 1.357 0.179 0.994 1.362 1.702
beta0_pH[3,1] 1.413 0.205 0.933 1.431 1.759
beta0_pH[4,1] 1.555 0.233 1.019 1.582 1.937
beta0_pH[5,1] -0.861 0.280 -1.454 -0.846 -0.361
beta0_pH[6,1] -0.652 0.414 -1.634 -0.584 -0.052
beta0_pH[7,1] -0.462 0.413 -1.369 -0.452 0.339
beta0_pH[8,1] -0.669 0.265 -1.286 -0.643 -0.211
beta0_pH[9,1] -0.653 0.286 -1.243 -0.633 -0.169
beta0_pH[10,1] 0.197 0.205 -0.246 0.212 0.558
beta0_pH[11,1] -0.076 0.165 -0.417 -0.069 0.234
beta0_pH[12,1] 0.488 0.188 0.108 0.489 0.852
beta0_pH[13,1] -0.002 0.141 -0.278 -0.004 0.276
beta0_pH[14,1] -0.320 0.164 -0.649 -0.320 -0.011
beta0_pH[15,1] -0.034 0.187 -0.406 -0.029 0.326
beta0_pH[16,1] -0.487 0.374 -1.458 -0.416 0.052
beta0_pH[1,2] 2.809 0.165 2.468 2.816 3.125
beta0_pH[2,2] 2.876 0.132 2.620 2.877 3.136
beta0_pH[3,2] 3.110 0.191 2.673 3.122 3.439
beta0_pH[4,2] 2.938 0.135 2.667 2.942 3.197
beta0_pH[5,2] 4.738 1.381 2.996 4.423 8.299
beta0_pH[6,2] 3.122 0.207 2.715 3.119 3.528
beta0_pH[7,2] 1.973 0.173 1.623 1.972 2.310
beta0_pH[8,2] 2.872 0.169 2.543 2.874 3.211
beta0_pH[9,2] 3.441 0.219 3.018 3.439 3.889
beta0_pH[10,2] 3.723 0.194 3.339 3.720 4.098
beta0_pH[11,2] -4.870 0.315 -5.510 -4.865 -4.229
beta0_pH[12,2] -4.799 0.406 -5.643 -4.790 -4.030
beta0_pH[13,2] -4.588 0.398 -5.369 -4.596 -3.751
beta0_pH[14,2] -5.625 0.495 -6.662 -5.597 -4.759
beta0_pH[15,2] -4.290 0.338 -4.939 -4.289 -3.615
beta0_pH[16,2] -4.877 0.389 -5.670 -4.857 -4.144
beta0_pH[1,3] 1.211 0.640 -0.161 1.176 2.155
beta0_pH[2,3] 2.202 0.163 1.883 2.203 2.524
beta0_pH[3,3] 2.522 0.147 2.234 2.517 2.805
beta0_pH[4,3] 2.957 0.161 2.647 2.954 3.285
beta0_pH[5,3] 1.417 1.740 -1.226 1.132 5.653
beta0_pH[6,3] -0.431 1.050 -2.501 -0.584 1.548
beta0_pH[7,3] -2.072 0.572 -3.338 -2.013 -1.141
beta0_pH[8,3] 0.283 0.202 -0.110 0.286 0.679
beta0_pH[9,3] -0.792 0.725 -2.845 -0.592 -0.003
beta0_pH[10,3] 0.315 0.812 -1.998 0.571 1.212
beta0_pH[11,3] -0.149 0.331 -0.776 -0.155 0.518
beta0_pH[12,3] -0.851 0.361 -1.592 -0.833 -0.220
beta0_pH[13,3] -0.119 0.316 -0.748 -0.115 0.500
beta0_pH[14,3] -0.266 0.260 -0.787 -0.268 0.244
beta0_pH[15,3] -0.677 0.286 -1.262 -0.668 -0.134
beta0_pH[16,3] -0.383 0.285 -0.951 -0.383 0.173
beta1_pH[1,1] 3.092 0.324 2.495 3.072 3.755
beta1_pH[2,1] 2.172 0.274 1.680 2.163 2.751
beta1_pH[3,1] 1.996 0.325 1.457 1.966 2.771
beta1_pH[4,1] 2.403 0.363 1.847 2.356 3.305
beta1_pH[5,1] 2.295 0.351 1.689 2.260 3.079
beta1_pH[6,1] 3.828 1.071 2.359 3.604 6.429
beta1_pH[7,1] 2.633 0.812 1.025 2.596 4.416
beta1_pH[8,1] 4.054 0.950 2.643 3.888 6.374
beta1_pH[9,1] 2.344 0.395 1.718 2.304 3.157
beta1_pH[10,1] 2.441 0.302 1.936 2.422 3.096
beta1_pH[11,1] 3.259 0.207 2.876 3.252 3.689
beta1_pH[12,1] 2.548 0.219 2.137 2.550 2.983
beta1_pH[13,1] 2.971 0.210 2.573 2.969 3.396
beta1_pH[14,1] 3.432 0.217 3.024 3.430 3.875
beta1_pH[15,1] 2.534 0.235 2.086 2.530 3.009
beta1_pH[16,1] 4.132 0.668 3.204 4.025 5.830
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.042 0.210 0.000 0.000 0.939
beta1_pH[4,2] 0.009 0.118 0.000 0.000 0.009
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.715 0.343 6.040 6.712 7.406
beta1_pH[12,2] 6.465 0.465 5.599 6.433 7.438
beta1_pH[13,2] 6.968 0.431 6.123 6.975 7.808
beta1_pH[14,2] 7.271 0.516 6.343 7.253 8.359
beta1_pH[15,2] 6.778 0.368 6.056 6.769 7.490
beta1_pH[16,2] 7.476 0.427 6.644 7.472 8.370
beta1_pH[1,3] 1.595 1.380 0.000 1.813 4.662
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.274 1.806 1.410 2.918 7.131
beta1_pH[6,3] 2.558 1.183 0.845 2.472 4.694
beta1_pH[7,3] 2.913 0.581 1.977 2.853 4.222
beta1_pH[8,3] 2.763 0.364 2.087 2.744 3.477
beta1_pH[9,3] 2.873 0.740 1.971 2.693 4.942
beta1_pH[10,3] 3.067 0.876 2.053 2.811 5.567
beta1_pH[11,3] 2.733 0.385 1.990 2.737 3.491
beta1_pH[12,3] 4.103 0.446 3.275 4.087 5.016
beta1_pH[13,3] 1.701 0.340 1.054 1.702 2.366
beta1_pH[14,3] 2.506 0.341 1.866 2.504 3.171
beta1_pH[15,3] 1.964 0.312 1.380 1.952 2.619
beta1_pH[16,3] 1.795 0.317 1.180 1.798 2.419
beta2_pH[1,1] 0.480 0.127 0.291 0.461 0.788
beta2_pH[2,1] 0.566 0.295 0.252 0.503 1.217
beta2_pH[3,1] 0.639 0.442 0.213 0.541 1.580
beta2_pH[4,1] 0.475 0.207 0.202 0.437 0.960
beta2_pH[5,1] 1.438 0.970 0.241 1.297 3.802
beta2_pH[6,1] 0.186 0.062 0.092 0.176 0.338
beta2_pH[7,1] 0.071 3.449 0.000 0.000 0.046
beta2_pH[8,1] 0.239 0.089 0.126 0.222 0.447
beta2_pH[9,1] 0.424 0.202 0.166 0.387 0.896
beta2_pH[10,1] 0.600 0.257 0.265 0.551 1.207
beta2_pH[11,1] 0.799 0.219 0.476 0.768 1.329
beta2_pH[12,1] 1.351 0.472 0.751 1.249 2.514
beta2_pH[13,1] 0.737 0.216 0.422 0.702 1.243
beta2_pH[14,1] 0.832 0.209 0.533 0.797 1.340
beta2_pH[15,1] 0.809 0.302 0.413 0.747 1.559
beta2_pH[16,1] 0.372 0.167 0.168 0.327 0.810
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -4.078 10.646 -20.220 -4.161 17.999
beta2_pH[4,2] -3.780 10.714 -21.601 -4.047 17.920
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -8.591 3.646 -17.280 -7.849 -3.896
beta2_pH[12,2] -7.017 4.263 -17.157 -6.389 -0.942
beta2_pH[13,2] -6.828 4.225 -17.213 -6.047 -1.639
beta2_pH[14,2] -7.513 3.923 -17.381 -6.637 -2.404
beta2_pH[15,2] -8.417 3.701 -17.605 -7.619 -3.610
beta2_pH[16,2] -8.663 3.708 -17.902 -7.844 -3.950
beta2_pH[1,3] 3.405 8.269 -14.981 1.935 21.689
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.292 6.371 0.255 6.977 23.169
beta2_pH[6,3] 8.306 6.417 0.168 7.169 23.829
beta2_pH[7,3] 8.039 6.369 0.612 6.674 23.311
beta2_pH[8,3] 9.313 5.839 1.171 8.322 23.228
beta2_pH[9,3] 7.936 6.482 0.331 6.766 22.963
beta2_pH[10,3] 7.641 6.709 0.350 6.396 23.490
beta2_pH[11,3] -2.475 2.251 -8.898 -1.718 -0.622
beta2_pH[12,3] -2.542 1.994 -8.327 -1.902 -0.915
beta2_pH[13,3] -3.107 2.459 -9.602 -2.284 -0.720
beta2_pH[14,3] -2.981 2.389 -9.753 -2.176 -0.882
beta2_pH[15,3] -3.237 2.537 -10.301 -2.356 -1.018
beta2_pH[16,3] -3.216 2.492 -10.278 -2.334 -0.917
beta3_pH[1,1] 35.839 0.816 34.277 35.814 37.522
beta3_pH[2,1] 33.553 1.151 31.541 33.457 36.056
beta3_pH[3,1] 33.669 1.111 31.645 33.634 35.981
beta3_pH[4,1] 33.798 1.218 31.521 33.721 36.280
beta3_pH[5,1] 27.781 1.184 26.470 27.501 31.086
beta3_pH[6,1] 38.714 3.049 32.936 38.566 44.820
beta3_pH[7,1] 30.617 7.905 18.478 30.115 44.989
beta3_pH[8,1] 40.056 2.056 36.453 39.793 44.601
beta3_pH[9,1] 30.677 1.502 28.079 30.569 33.977
beta3_pH[10,1] 32.662 0.919 30.908 32.630 34.542
beta3_pH[11,1] 30.361 0.474 29.434 30.349 31.303
beta3_pH[12,1] 30.170 0.402 29.368 30.175 30.939
beta3_pH[13,1] 33.148 0.576 32.040 33.133 34.329
beta3_pH[14,1] 32.026 0.449 31.184 32.017 32.939
beta3_pH[15,1] 31.163 0.653 29.815 31.165 32.436
beta3_pH[16,1] 32.055 1.028 30.279 31.939 34.437
beta3_pH[1,2] 29.867 8.070 18.434 29.088 45.031
beta3_pH[2,2] 29.715 7.876 18.401 28.718 44.952
beta3_pH[3,2] 30.393 8.042 18.520 29.511 44.910
beta3_pH[4,2] 30.141 8.137 18.506 29.153 45.081
beta3_pH[5,2] 30.224 7.998 18.500 29.316 44.910
beta3_pH[6,2] 29.958 8.021 18.392 28.760 44.898
beta3_pH[7,2] 29.833 8.076 18.430 28.722 45.097
beta3_pH[8,2] 29.800 8.010 18.364 28.938 44.823
beta3_pH[9,2] 29.975 7.962 18.413 29.198 44.890
beta3_pH[10,2] 30.066 7.980 18.448 29.059 44.992
beta3_pH[11,2] 43.405 0.173 43.126 43.385 43.775
beta3_pH[12,2] 43.195 0.185 42.928 43.153 43.685
beta3_pH[13,2] 43.858 0.143 43.487 43.895 44.040
beta3_pH[14,2] 43.307 0.196 43.055 43.259 43.789
beta3_pH[15,2] 43.409 0.188 43.112 43.388 43.798
beta3_pH[16,2] 43.494 0.179 43.170 43.489 43.827
beta3_pH[1,3] 35.920 6.645 19.201 39.074 43.852
beta3_pH[2,3] 30.141 7.942 18.536 29.301 44.717
beta3_pH[3,3] 30.312 8.035 18.421 29.750 44.887
beta3_pH[4,3] 29.883 7.917 18.427 28.872 44.733
beta3_pH[5,3] 27.170 6.715 18.331 25.944 42.497
beta3_pH[6,3] 28.179 7.166 18.673 25.790 44.388
beta3_pH[7,3] 26.559 0.958 24.998 26.424 28.799
beta3_pH[8,3] 41.492 0.303 40.999 41.490 41.966
beta3_pH[9,3] 32.919 1.649 27.811 33.480 34.316
beta3_pH[10,3] 35.542 1.295 32.071 36.006 36.873
beta3_pH[11,3] 41.784 0.814 40.143 41.814 43.258
beta3_pH[12,3] 41.723 0.391 40.940 41.737 42.490
beta3_pH[13,3] 42.755 0.932 40.988 42.779 44.902
beta3_pH[14,3] 41.085 0.572 39.880 41.118 42.150
beta3_pH[15,3] 42.653 0.681 41.111 42.749 43.754
beta3_pH[16,3] 42.882 0.750 41.134 42.995 44.065
beta0_pelagic[1] 2.203 0.130 1.954 2.204 2.455
beta0_pelagic[2] 1.516 0.125 1.264 1.521 1.754
beta0_pelagic[3] -0.292 0.691 -1.860 -0.127 0.735
beta0_pelagic[4] -0.151 0.864 -2.055 0.083 1.055
beta0_pelagic[5] 1.174 0.249 0.663 1.178 1.651
beta0_pelagic[6] 1.473 0.269 0.907 1.495 1.969
beta0_pelagic[7] 1.638 0.215 1.253 1.622 2.102
beta0_pelagic[8] 1.749 0.205 1.356 1.741 2.184
beta0_pelagic[9] 2.513 0.313 1.879 2.521 3.087
beta0_pelagic[10] 2.535 0.202 2.121 2.546 2.903
beta0_pelagic[11] 0.129 0.423 -0.770 0.238 0.731
beta0_pelagic[12] 1.682 0.145 1.396 1.683 1.961
beta0_pelagic[13] 0.318 0.201 -0.139 0.332 0.669
beta0_pelagic[14] -0.088 0.275 -0.692 -0.065 0.378
beta0_pelagic[15] -0.248 0.141 -0.527 -0.246 0.019
beta0_pelagic[16] 0.350 0.221 -0.218 0.387 0.672
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.806 1.122 0.002 1.605 4.381
beta1_pelagic[4] 1.569 1.254 0.000 1.201 5.029
beta1_pelagic[5] -0.076 0.317 -0.683 -0.080 0.537
beta1_pelagic[6] -0.108 0.452 -0.858 -0.160 0.750
beta1_pelagic[7] -0.012 0.308 -0.601 -0.014 0.574
beta1_pelagic[8] 0.008 0.283 -0.540 0.007 0.564
beta1_pelagic[9] 0.183 0.476 -0.743 0.284 0.925
beta1_pelagic[10] 0.060 0.265 -0.469 0.063 0.590
beta1_pelagic[11] 3.483 1.034 2.227 3.256 5.947
beta1_pelagic[12] 2.750 0.301 2.187 2.747 3.347
beta1_pelagic[13] 2.886 0.710 1.831 2.779 4.599
beta1_pelagic[14] 4.301 1.021 2.843 4.086 6.722
beta1_pelagic[15] 2.908 0.259 2.385 2.908 3.408
beta1_pelagic[16] 3.439 0.744 2.690 3.247 5.764
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 6.597 82.808 0.024 0.143 11.622
beta2_pelagic[4] 3.844 12.585 0.008 0.387 13.156
beta2_pelagic[5] -0.010 0.665 -1.348 -0.020 1.394
beta2_pelagic[6] -0.110 0.690 -1.527 -0.150 1.318
beta2_pelagic[7] -0.009 0.653 -1.432 -0.003 1.331
beta2_pelagic[8] 0.000 0.647 -1.389 0.007 1.427
beta2_pelagic[9] 0.168 0.685 -1.278 0.233 1.576
beta2_pelagic[10] 0.030 0.621 -1.317 0.020 1.365
beta2_pelagic[11] 2.235 4.204 0.121 0.333 14.444
beta2_pelagic[12] 6.883 5.463 1.324 5.259 22.378
beta2_pelagic[13] 0.928 1.925 0.191 0.487 5.389
beta2_pelagic[14] 0.329 0.154 0.158 0.294 0.733
beta2_pelagic[15] 6.767 4.845 1.619 5.456 20.235
beta2_pelagic[16] 5.691 5.568 0.230 4.383 21.163
beta3_pelagic[1] 29.991 7.852 18.512 29.085 44.911
beta3_pelagic[2] 29.918 7.998 18.484 28.840 45.144
beta3_pelagic[3] 30.196 6.499 19.291 29.587 44.088
beta3_pelagic[4] 26.073 5.702 18.656 25.131 42.458
beta3_pelagic[5] 29.978 8.277 18.432 28.465 45.205
beta3_pelagic[6] 31.922 6.747 18.955 31.979 44.207
beta3_pelagic[7] 29.679 7.636 18.477 28.848 44.931
beta3_pelagic[8] 29.492 7.916 18.490 28.198 44.586
beta3_pelagic[9] 30.799 6.306 19.061 30.637 43.471
beta3_pelagic[10] 29.520 8.092 18.378 28.180 45.099
beta3_pelagic[11] 42.419 1.794 37.877 42.995 45.192
beta3_pelagic[12] 43.455 0.264 43.009 43.443 43.942
beta3_pelagic[13] 42.775 1.297 40.407 42.717 45.519
beta3_pelagic[14] 42.412 1.645 39.126 42.374 45.538
beta3_pelagic[15] 43.201 0.240 42.677 43.192 43.672
beta3_pelagic[16] 43.186 0.648 41.566 43.236 44.545
mu_beta0_pelagic[1] 0.762 1.053 -1.656 0.860 2.719
mu_beta0_pelagic[2] 1.809 0.399 0.959 1.831 2.550
mu_beta0_pelagic[3] 0.343 0.459 -0.613 0.354 1.243
tau_beta0_pelagic[1] 0.602 0.731 0.052 0.350 2.563
tau_beta0_pelagic[2] 2.702 2.970 0.256 1.918 9.480
tau_beta0_pelagic[3] 1.607 1.205 0.202 1.294 4.685
beta0_yellow[1] -0.526 0.182 -0.914 -0.515 -0.206
beta0_yellow[2] 0.511 0.169 0.181 0.517 0.812
beta0_yellow[3] -0.290 0.182 -0.649 -0.287 0.049
beta0_yellow[4] 0.858 0.256 0.146 0.895 1.219
beta0_yellow[5] -1.370 0.420 -2.182 -1.380 -0.539
beta0_yellow[6] -0.234 0.557 -1.609 -0.144 0.527
beta0_yellow[7] 1.045 0.158 0.737 1.042 1.357
beta0_yellow[8] 0.947 0.300 0.075 0.995 1.302
beta0_yellow[9] -0.593 0.916 -2.671 -0.536 0.854
beta0_yellow[10] 0.219 0.159 -0.091 0.217 0.520
beta0_yellow[11] -1.947 0.436 -2.764 -1.953 -1.085
beta0_yellow[12] -3.740 0.432 -4.632 -3.726 -2.945
beta0_yellow[13] -3.782 0.487 -4.820 -3.751 -2.915
beta0_yellow[14] -2.099 0.593 -3.096 -2.167 -0.464
beta0_yellow[15] -2.839 0.431 -3.758 -2.811 -2.060
beta0_yellow[16] -2.420 0.465 -3.386 -2.403 -1.530
beta1_yellow[1] 0.567 0.826 0.000 0.382 2.277
beta1_yellow[2] 1.047 0.393 0.563 1.000 1.760
beta1_yellow[3] 0.648 0.278 0.095 0.646 1.154
beta1_yellow[4] 1.330 0.679 0.644 1.168 3.588
beta1_yellow[5] 3.514 1.469 1.726 3.305 7.136
beta1_yellow[6] 4.063 1.205 2.309 3.851 6.906
beta1_yellow[7] 7.391 6.458 2.305 5.185 25.866
beta1_yellow[8] 4.128 5.526 0.035 3.092 12.704
beta1_yellow[9] 3.361 2.103 0.115 3.127 7.706
beta1_yellow[10] 2.610 0.577 1.639 2.576 3.811
beta1_yellow[11] 2.092 0.440 1.223 2.101 2.935
beta1_yellow[12] 2.526 0.447 1.734 2.503 3.466
beta1_yellow[13] 2.906 0.486 2.033 2.871 3.912
beta1_yellow[14] 2.181 0.567 0.911 2.217 3.189
beta1_yellow[15] 2.090 0.430 1.304 2.073 3.001
beta1_yellow[16] 2.180 0.466 1.268 2.172 3.130
beta2_yellow[1] -4.469 3.349 -11.921 -3.813 -0.052
beta2_yellow[2] -4.332 3.202 -11.680 -3.747 -0.217
beta2_yellow[3] -4.308 3.457 -12.561 -3.509 -0.177
beta2_yellow[4] -3.723 3.215 -10.871 -2.914 -0.107
beta2_yellow[5] -4.188 2.959 -11.185 -3.444 -0.515
beta2_yellow[6] 0.181 0.391 0.090 0.209 0.248
beta2_yellow[7] -4.658 2.837 -11.644 -4.046 -1.040
beta2_yellow[8] -3.492 2.981 -10.970 -2.744 -0.034
beta2_yellow[9] -0.768 2.474 -9.018 0.141 0.244
beta2_yellow[10] -4.149 2.930 -11.638 -3.434 -0.639
beta2_yellow[11] -5.290 2.907 -11.929 -4.780 -1.186
beta2_yellow[12] -5.685 2.903 -12.550 -5.146 -1.523
beta2_yellow[13] -5.250 2.624 -11.400 -4.737 -1.613
beta2_yellow[14] -5.621 3.065 -12.506 -5.146 -0.843
beta2_yellow[15] -5.163 3.003 -12.343 -4.544 -1.113
beta2_yellow[16] -5.685 2.983 -12.473 -5.093 -1.472
beta3_yellow[1] 27.252 7.577 18.309 24.211 44.169
beta3_yellow[2] 29.091 1.792 25.839 28.891 32.726
beta3_yellow[3] 32.892 3.013 25.289 32.874 39.092
beta3_yellow[4] 28.883 3.278 22.428 27.916 35.919
beta3_yellow[5] 33.239 1.358 30.137 33.308 35.134
beta3_yellow[6] 41.969 2.816 35.505 42.305 45.774
beta3_yellow[7] 19.851 0.660 18.444 19.908 20.906
beta3_yellow[8] 24.799 5.134 18.386 24.165 41.475
beta3_yellow[9] 35.331 8.477 18.523 37.910 45.526
beta3_yellow[10] 29.178 0.763 27.245 29.327 30.016
beta3_yellow[11] 45.314 0.518 44.075 45.396 45.968
beta3_yellow[12] 43.321 0.368 42.575 43.287 44.060
beta3_yellow[13] 44.913 0.379 44.036 44.979 45.567
beta3_yellow[14] 43.885 2.033 34.753 44.185 45.827
beta3_yellow[15] 45.153 0.533 44.169 45.103 45.968
beta3_yellow[16] 44.554 0.660 43.367 44.526 45.857
mu_beta0_yellow[1] 0.120 0.537 -0.995 0.117 1.214
mu_beta0_yellow[2] 0.017 0.569 -1.165 0.025 1.133
mu_beta0_yellow[3] -2.447 0.652 -3.489 -2.530 -0.845
tau_beta0_yellow[1] 1.809 2.125 0.099 1.160 7.125
tau_beta0_yellow[2] 0.885 0.753 0.102 0.677 2.878
tau_beta0_yellow[3] 1.409 2.786 0.090 0.871 5.465
beta0_black[1] -0.074 0.156 -0.379 -0.075 0.237
beta0_black[2] 1.916 0.126 1.673 1.917 2.163
beta0_black[3] 1.317 0.135 1.052 1.316 1.582
beta0_black[4] 2.429 0.134 2.169 2.430 2.695
beta0_black[5] 1.656 1.968 -2.369 1.678 5.837
beta0_black[6] 1.618 1.939 -2.726 1.670 5.702
beta0_black[7] 1.632 1.904 -2.571 1.682 5.482
beta0_black[8] 1.294 0.226 0.844 1.293 1.748
beta0_black[9] 2.439 0.250 1.954 2.433 2.936
beta0_black[10] 1.475 0.130 1.223 1.472 1.736
beta0_black[11] 3.489 0.150 3.195 3.487 3.781
beta0_black[12] 4.858 0.178 4.510 4.859 5.222
beta0_black[13] -0.118 0.243 -0.624 -0.110 0.332
beta0_black[14] 2.853 0.158 2.537 2.857 3.163
beta0_black[15] 1.291 0.155 0.985 1.288 1.597
beta0_black[16] 4.270 0.158 3.964 4.272 4.575
beta2_black[1] 3.508 2.290 0.735 2.970 9.100
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.095 1.721 -6.965 -1.535 -0.415
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.665 1.352 39.768 41.856 43.083
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.223 0.774 37.477 39.311 40.500
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.265 0.192 -0.644 -0.261 0.108
beta4_black[2] 0.236 0.178 -0.122 0.236 0.582
beta4_black[3] -0.933 0.195 -1.318 -0.932 -0.562
beta4_black[4] 0.425 0.221 -0.008 0.423 0.863
beta4_black[5] 0.236 2.461 -4.582 0.175 5.622
beta4_black[6] 0.220 2.402 -4.806 0.167 5.057
beta4_black[7] 0.211 2.373 -4.473 0.140 5.155
beta4_black[8] -0.693 0.381 -1.451 -0.691 0.042
beta4_black[9] 1.503 1.046 -0.091 1.367 3.844
beta4_black[10] 0.025 0.187 -0.343 0.026 0.386
beta4_black[11] -0.701 0.212 -1.127 -0.701 -0.301
beta4_black[12] 0.177 0.326 -0.438 0.175 0.844
beta4_black[13] -1.187 0.227 -1.632 -1.189 -0.754
beta4_black[14] -0.181 0.238 -0.639 -0.184 0.277
beta4_black[15] -0.886 0.206 -1.305 -0.886 -0.494
beta4_black[16] -0.593 0.225 -1.030 -0.587 -0.150
mu_beta0_black[1] 1.275 0.906 -0.672 1.324 3.042
mu_beta0_black[2] 1.613 0.891 -0.485 1.680 3.389
mu_beta0_black[3] 2.499 1.004 0.300 2.548 4.349
tau_beta0_black[1] 0.619 0.583 0.056 0.437 2.151
tau_beta0_black[2] 1.964 3.731 0.057 0.875 10.286
tau_beta0_black[3] 0.237 0.158 0.051 0.199 0.646
beta0_dsr[11] -2.901 0.287 -3.474 -2.902 -2.326
beta0_dsr[12] 4.549 0.278 4.025 4.547 5.091
beta0_dsr[13] -1.344 0.308 -1.934 -1.341 -0.775
beta0_dsr[14] -3.654 0.508 -4.640 -3.650 -2.670
beta0_dsr[15] -1.947 0.283 -2.510 -1.941 -1.400
beta0_dsr[16] -2.977 0.363 -3.688 -2.970 -2.272
beta1_dsr[11] 4.833 0.299 4.250 4.831 5.412
beta1_dsr[12] 6.813 10.120 2.203 5.009 21.497
beta1_dsr[13] 2.854 0.338 2.278 2.841 3.480
beta1_dsr[14] 6.320 0.536 5.260 6.321 7.378
beta1_dsr[15] 3.342 0.291 2.777 3.343 3.929
beta1_dsr[16] 5.796 0.379 5.065 5.796 6.552
beta2_dsr[11] -8.380 2.398 -14.159 -8.066 -4.638
beta2_dsr[12] -7.186 2.728 -13.506 -6.938 -2.572
beta2_dsr[13] -6.559 2.787 -12.472 -6.454 -1.458
beta2_dsr[14] -6.152 2.771 -12.184 -5.997 -1.705
beta2_dsr[15] -7.883 2.448 -13.554 -7.555 -4.023
beta2_dsr[16] -7.985 2.342 -13.460 -7.655 -4.363
beta3_dsr[11] 43.490 0.148 43.216 43.489 43.769
beta3_dsr[12] 33.963 0.741 32.119 34.102 34.808
beta3_dsr[13] 43.242 0.276 42.805 43.191 43.852
beta3_dsr[14] 43.354 0.243 43.070 43.283 43.970
beta3_dsr[15] 43.512 0.186 43.166 43.511 43.845
beta3_dsr[16] 43.439 0.160 43.175 43.426 43.764
beta4_dsr[11] 0.589 0.217 0.184 0.590 1.021
beta4_dsr[12] 0.239 0.447 -0.665 0.232 1.166
beta4_dsr[13] -0.166 0.215 -0.603 -0.162 0.236
beta4_dsr[14] 0.149 0.250 -0.335 0.149 0.628
beta4_dsr[15] 0.727 0.214 0.311 0.722 1.136
beta4_dsr[16] 0.144 0.226 -0.306 0.145 0.594
beta0_slope[11] -1.870 0.166 -2.202 -1.868 -1.545
beta0_slope[12] -4.814 0.269 -5.354 -4.808 -4.316
beta0_slope[13] -1.291 0.192 -1.706 -1.281 -0.944
beta0_slope[14] -2.645 0.177 -2.990 -2.644 -2.298
beta0_slope[15] -1.321 0.168 -1.642 -1.324 -0.987
beta0_slope[16] -2.679 0.172 -3.022 -2.682 -2.342
beta1_slope[11] 4.501 0.297 3.926 4.502 5.082
beta1_slope[12] 4.438 0.497 3.493 4.428 5.412
beta1_slope[13] 2.783 0.445 2.124 2.736 3.959
beta1_slope[14] 6.501 0.521 5.504 6.505 7.528
beta1_slope[15] 3.062 0.277 2.507 3.066 3.600
beta1_slope[16] 5.319 0.362 4.625 5.320 6.019
beta2_slope[11] 8.004 2.354 4.519 7.637 13.458
beta2_slope[12] 6.465 2.721 1.519 6.367 12.334
beta2_slope[13] 5.787 2.936 0.467 5.811 11.843
beta2_slope[14] 6.402 2.445 2.341 6.188 11.882
beta2_slope[15] 7.612 2.414 3.862 7.262 13.407
beta2_slope[16] 7.536 2.254 3.945 7.220 12.871
beta3_slope[11] 43.451 0.148 43.185 43.444 43.746
beta3_slope[12] 43.290 0.258 42.849 43.256 43.819
beta3_slope[13] 43.542 0.419 42.860 43.571 44.143
beta3_slope[14] 43.314 0.169 43.093 43.273 43.731
beta3_slope[15] 43.487 0.186 43.157 43.483 43.836
beta3_slope[16] 43.397 0.161 43.139 43.382 43.739
beta4_slope[11] -0.743 0.217 -1.172 -0.736 -0.344
beta4_slope[12] -1.156 0.503 -2.290 -1.101 -0.319
beta4_slope[13] 0.004 0.220 -0.400 -0.004 0.448
beta4_slope[14] -0.119 0.252 -0.616 -0.122 0.393
beta4_slope[15] -0.803 0.216 -1.235 -0.799 -0.389
beta4_slope[16] -0.278 0.223 -0.712 -0.284 0.149
sigma_H[1] 0.200 0.053 0.101 0.196 0.319
sigma_H[2] 0.171 0.031 0.118 0.168 0.238
sigma_H[3] 0.194 0.042 0.118 0.192 0.283
sigma_H[4] 0.421 0.077 0.297 0.412 0.591
sigma_H[5] 0.997 0.208 0.611 0.987 1.419
sigma_H[6] 0.383 0.203 0.029 0.377 0.809
sigma_H[7] 0.301 0.060 0.207 0.294 0.444
sigma_H[8] 0.417 0.087 0.281 0.406 0.608
sigma_H[9] 0.525 0.127 0.329 0.508 0.808
sigma_H[10] 0.215 0.043 0.142 0.211 0.307
sigma_H[11] 0.278 0.047 0.200 0.275 0.385
sigma_H[12] 0.432 0.164 0.208 0.410 0.762
sigma_H[13] 0.215 0.037 0.150 0.211 0.296
sigma_H[14] 0.511 0.094 0.346 0.507 0.714
sigma_H[15] 0.247 0.041 0.180 0.243 0.337
sigma_H[16] 0.225 0.044 0.152 0.220 0.326
lambda_H[1] 2.940 3.702 0.172 1.697 14.143
lambda_H[2] 8.241 7.728 0.740 5.967 29.182
lambda_H[3] 6.381 10.091 0.246 3.197 31.866
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 3.630 7.479 0.038 1.109 23.585
lambda_H[6] 6.622 13.630 0.007 0.866 39.030
lambda_H[7] 0.013 0.009 0.002 0.011 0.035
lambda_H[8] 8.305 10.642 0.121 4.686 36.698
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.334 0.979 0.030 0.205 1.132
lambda_H[11] 0.251 0.347 0.011 0.129 1.223
lambda_H[12] 4.828 6.684 0.177 2.657 23.107
lambda_H[13] 3.476 3.258 0.245 2.505 11.907
lambda_H[14] 3.427 4.126 0.230 2.098 14.481
lambda_H[15] 0.025 0.038 0.003 0.017 0.097
lambda_H[16] 0.785 1.041 0.047 0.425 3.423
mu_lambda_H[1] 4.336 1.883 1.250 4.142 8.442
mu_lambda_H[2] 3.845 1.928 0.659 3.678 7.921
mu_lambda_H[3] 3.495 1.845 0.730 3.212 7.695
sigma_lambda_H[1] 8.674 4.400 2.034 7.880 18.366
sigma_lambda_H[2] 8.345 4.609 1.064 7.768 18.249
sigma_lambda_H[3] 6.275 3.999 0.977 5.436 16.107
beta_H[1,1] 6.916 1.020 4.501 7.078 8.455
beta_H[2,1] 9.879 0.506 8.750 9.910 10.791
beta_H[3,1] 7.983 0.778 6.087 8.080 9.196
beta_H[4,1] 9.188 7.715 -6.041 9.491 24.385
beta_H[5,1] 0.150 2.248 -4.625 0.359 3.894
beta_H[6,1] 3.036 4.056 -7.242 4.517 7.436
beta_H[7,1] 0.555 5.703 -11.432 0.806 10.656
beta_H[8,1] 1.393 4.016 -2.305 1.282 3.461
beta_H[9,1] 13.045 5.685 1.746 13.053 24.447
beta_H[10,1] 7.086 1.689 3.545 7.159 10.262
beta_H[11,1] 5.047 3.560 -2.962 5.785 10.046
beta_H[12,1] 2.610 1.084 0.746 2.526 5.025
beta_H[13,1] 9.042 0.914 7.162 9.113 10.514
beta_H[14,1] 2.227 1.041 0.232 2.222 4.427
beta_H[15,1] -6.164 3.854 -13.201 -6.400 2.287
beta_H[16,1] 3.405 2.608 -1.105 3.141 9.555
beta_H[1,2] 7.905 0.243 7.413 7.908 8.377
beta_H[2,2] 10.025 0.135 9.760 10.025 10.287
beta_H[3,2] 8.950 0.195 8.565 8.949 9.347
beta_H[4,2] 3.613 1.475 0.840 3.539 6.712
beta_H[5,2] 1.947 0.937 0.050 1.975 3.712
beta_H[6,2] 5.767 1.031 3.288 5.932 7.393
beta_H[7,2] 2.662 1.055 0.771 2.603 4.956
beta_H[8,2] 3.011 1.134 1.444 3.155 4.234
beta_H[9,2] 3.494 1.106 1.362 3.454 5.796
beta_H[10,2] 8.204 0.343 7.521 8.206 8.876
beta_H[11,2] 9.776 0.644 8.828 9.642 11.216
beta_H[12,2] 3.947 0.378 3.244 3.930 4.742
beta_H[13,2] 9.118 0.253 8.653 9.103 9.603
beta_H[14,2] 4.020 0.354 3.358 4.018 4.735
beta_H[15,2] 11.383 0.692 9.903 11.421 12.672
beta_H[16,2] 4.528 0.816 3.028 4.525 6.168
beta_H[1,3] 8.472 0.240 8.041 8.453 8.983
beta_H[2,3] 10.069 0.116 9.836 10.068 10.300
beta_H[3,3] 9.615 0.163 9.310 9.614 9.946
beta_H[4,3] -2.543 0.865 -4.290 -2.534 -0.858
beta_H[5,3] 3.815 0.600 2.601 3.829 4.954
beta_H[6,3] 8.018 1.197 6.330 7.679 10.587
beta_H[7,3] -2.773 0.626 -4.017 -2.769 -1.591
beta_H[8,3] 5.249 0.513 4.651 5.184 6.171
beta_H[9,3] -2.832 0.728 -4.296 -2.821 -1.432
beta_H[10,3] 8.676 0.274 8.133 8.676 9.212
beta_H[11,3] 8.534 0.290 7.889 8.560 9.037
beta_H[12,3] 5.243 0.335 4.410 5.286 5.771
beta_H[13,3] 8.841 0.179 8.479 8.846 9.178
beta_H[14,3] 5.712 0.281 5.062 5.737 6.212
beta_H[15,3] 10.358 0.317 9.733 10.368 10.969
beta_H[16,3] 6.213 0.620 4.829 6.284 7.222
beta_H[1,4] 8.262 0.179 7.884 8.274 8.581
beta_H[2,4] 10.130 0.122 9.868 10.136 10.359
beta_H[3,4] 10.120 0.163 9.766 10.133 10.407
beta_H[4,4] 11.799 0.447 10.924 11.795 12.672
beta_H[5,4] 5.468 0.737 4.239 5.390 7.177
beta_H[6,4] 7.067 0.941 4.934 7.334 8.374
beta_H[7,4] 8.223 0.330 7.578 8.228 8.876
beta_H[8,4] 6.710 0.249 6.249 6.720 7.136
beta_H[9,4] 7.195 0.472 6.247 7.194 8.164
beta_H[10,4] 7.764 0.237 7.310 7.760 8.225
beta_H[11,4] 9.385 0.201 8.997 9.382 9.784
beta_H[12,4] 7.149 0.219 6.735 7.143 7.618
beta_H[13,4] 9.046 0.143 8.755 9.045 9.320
beta_H[14,4] 7.726 0.222 7.307 7.721 8.169
beta_H[15,4] 9.476 0.231 9.024 9.473 9.937
beta_H[16,4] 9.353 0.238 8.937 9.338 9.848
beta_H[1,5] 8.976 0.147 8.687 8.981 9.260
beta_H[2,5] 10.785 0.094 10.605 10.782 10.979
beta_H[3,5] 10.918 0.170 10.615 10.908 11.265
beta_H[4,5] 8.393 0.465 7.523 8.390 9.348
beta_H[5,5] 5.415 0.576 4.053 5.451 6.429
beta_H[6,5] 8.827 0.649 7.900 8.676 10.361
beta_H[7,5] 6.795 0.333 6.145 6.789 7.491
beta_H[8,5] 8.205 0.215 7.849 8.191 8.640
beta_H[9,5] 8.219 0.483 7.239 8.222 9.175
beta_H[10,5] 10.080 0.228 9.635 10.083 10.522
beta_H[11,5] 11.513 0.225 11.070 11.510 11.956
beta_H[12,5] 8.483 0.203 8.077 8.483 8.882
beta_H[13,5] 10.013 0.130 9.759 10.013 10.270
beta_H[14,5] 9.196 0.235 8.788 9.183 9.710
beta_H[15,5] 11.165 0.242 10.678 11.163 11.631
beta_H[16,5] 9.911 0.184 9.526 9.917 10.258
beta_H[1,6] 10.189 0.192 9.865 10.174 10.615
beta_H[2,6] 11.510 0.107 11.301 11.511 11.719
beta_H[3,6] 10.811 0.157 10.474 10.822 11.101
beta_H[4,6] 12.854 0.820 11.198 12.891 14.445
beta_H[5,6] 5.879 0.602 4.704 5.874 7.043
beta_H[6,6] 8.769 0.700 6.881 8.906 9.771
beta_H[7,6] 9.825 0.553 8.738 9.816 10.936
beta_H[8,6] 9.510 0.284 9.023 9.527 9.957
beta_H[9,6] 8.457 0.808 6.894 8.446 10.061
beta_H[10,6] 9.524 0.317 8.829 9.553 10.072
beta_H[11,6] 10.809 0.359 10.046 10.830 11.470
beta_H[12,6] 9.369 0.253 8.879 9.361 9.883
beta_H[13,6] 11.051 0.164 10.768 11.039 11.399
beta_H[14,6] 9.821 0.305 9.210 9.826 10.430
beta_H[15,6] 10.836 0.425 10.006 10.837 11.655
beta_H[16,6] 10.537 0.242 10.020 10.551 10.994
beta_H[1,7] 10.875 0.880 8.642 10.986 12.305
beta_H[2,7] 12.196 0.439 11.326 12.196 13.054
beta_H[3,7] 10.542 0.660 9.099 10.618 11.690
beta_H[4,7] 2.651 4.131 -5.324 2.545 10.806
beta_H[5,7] 6.423 1.759 2.978 6.381 10.387
beta_H[6,7] 9.653 2.514 4.932 9.548 16.440
beta_H[7,7] 10.676 2.803 5.210 10.659 16.104
beta_H[8,7] 10.939 1.056 9.378 10.897 12.553
beta_H[9,7] 4.493 4.138 -3.870 4.457 12.506
beta_H[10,7] 9.774 1.436 7.220 9.690 12.914
beta_H[11,7] 11.027 1.750 7.794 10.926 14.797
beta_H[12,7] 9.967 0.992 7.895 10.042 11.648
beta_H[13,7] 11.646 0.733 9.925 11.745 12.793
beta_H[14,7] 10.435 0.981 8.427 10.482 12.189
beta_H[15,7] 12.020 2.202 7.793 12.014 16.426
beta_H[16,7] 12.279 1.268 10.183 12.105 15.205
beta0_H[1] 9.090 13.114 -17.693 9.177 36.766
beta0_H[2] 10.521 6.535 -2.540 10.568 23.349
beta0_H[3] 9.705 9.830 -10.233 9.842 29.116
beta0_H[4] 11.832 180.116 -346.141 12.478 370.041
beta0_H[5] 4.404 22.853 -42.389 4.261 52.701
beta0_H[6] 8.147 51.954 -101.850 7.750 123.028
beta0_H[7] 6.179 132.610 -255.299 4.170 282.760
beta0_H[8] 6.245 33.862 -15.029 6.430 26.488
beta0_H[9] 3.671 120.201 -239.932 7.121 245.903
beta0_H[10] 9.303 32.691 -55.712 8.794 77.386
beta0_H[11] 9.085 54.873 -99.970 10.065 112.763
beta0_H[12] 6.473 11.600 -15.645 6.664 29.168
beta0_H[13] 9.774 10.714 -10.755 9.794 31.153
beta0_H[14] 7.220 12.479 -15.039 7.092 32.569
beta0_H[15] 9.348 105.845 -207.609 8.854 229.233
beta0_H[16] 8.382 25.165 -44.420 8.013 62.392